Mitigation of stochastic diffusion losses in optimized stellarators

Abstract

Abstract. The stochastic diffusion (SD) resulting from collisionless transformations between locally trapped and locally passing orbits may lead to a significant loss of energetic particles from stellarator plasmas (Beidler C D et al 2001 Phys. Plasmas 8 2731. In this work, a method to mitigate the consequences of SD is suggested. The method consists in changing the shapes of the separatrices between the locally trapped and locally passing states so that most separatrices do not cross the plasma boundary, which is achieved with a suitable modification of the magnetic configuration. It is demonstrated analytically that in this way the particle loss because of the SD may be reduced significantly, even though the SD still occurs. In particular, it is possible to protect fast particles inside a certain radius from SD loss. It is shown that a variation of the electric field can also affect the SD loss. The modifications of the magnetic configuration and the electric field required for the mitigation are quantified for a configuration of the stellarator Wendelstein 7-X.

Confinement of transitioning particles in bi-helical Wendelstein-type configurations

“…The numerical calculation has also demonstrated a possibility to prevent the escape of particles to the wall by making the separatrix between the locally trapped and passing states () closed, as was proposed in Tykhyy et al. (2007). It was concluded in Kolesnichenko et al.…”

“…If the separatrix of a given particle is closed within the plasma volume, the particle will be confined despite undergoing stochastic diffusion, and vice versa (Tykhyy et al. 2007) (provided that drift orbits are closer to than the separatrix, as is the case in Wendelstein-type configurations; however, it is desirable for drift orbits to be close to from many considerations and this property is one of stellarator optimisation criteria). Note that minor harmonics of omitted from (2.1) may cause particles which are confined in the model magnetic field to be lost from the plasma.…”

“…Some of the approaches which have been suggested to deal with the delayed losses of these transitioning particles, such as modification of the mirror harmonic (Tykhyy et al. 2007), control of radial electric field (Tykhyy et al. 2007; Tykhyy & Kolesnichenko 2021), rely on controlling the shape of the separatrix between two types of trapped particle orbits: those trapped in local magnetic wells and those trapped by the toroidal inhomogeneity of the magnetic field.…”

“…2007), control of radial electric field (Tykhyy et al. 2007; Tykhyy & Kolesnichenko 2021), rely on controlling the shape of the separatrix between two types of trapped particle orbits: those trapped in local magnetic wells and those trapped by the toroidal inhomogeneity of the magnetic field. However, there are difficulties involved in these approaches, as, e.g., the radial electric field in stellarators arises due to the neoclassical fluxes and may not be readily modified to suit the requirements of separatrix control for energetic particle loss mitigation.…”

Statistical description of collisionlessα-particle transport in cases of broken symmetry: from ITER to quasi-toroidally symmetric stellarators

“…The dif-fusion coefficient for the transition from trapped to passing particles and vice versa, defined as D =< ∆r 2 > /τ , could reach 100 m 2 /s, where the numerator is the change in a radial coordinate caused by orbit transformation, and the denominator is an average between the trapping and passing times τ = (τ trapped +τ passing )/2. The possibility of improving the transition particles confinement by radial electric field was studied in [82,83], while the curing effect of transition particles on plasma stability is discussed in [84].…”